# Some observations on numbers in short intervals

## Main Article Content

## Abstract

We obtain some results about the primes and the prime factorizations of the positive integers in the interval (*x*, *x*+*x*^{θ}], where *0*<θ<*1*. We also obtain some results about the primes and the prime factorizations of the positive integers in the interval (*x*, *x*+*f*(*x*)], where *f*(*x*) is a function of slow increase. For instance, *f*(*x*)=log^{α}*x*, where α>*0*.

## Article Details

How to Cite

*Gulf Journal of Mathematics*,

*13*(1), 25-40. Retrieved from https://gjom.org/index.php/gjom/article/view/925

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